18((3x-4)(3x-4))=108

Solution for 18((3x-4)(3x-4))=108 equation:

Simplifying
18((3x + -4)(3x + -4)) = 108

Reorder the terms:
18((-4 + 3x)(3x + -4)) = 108

Reorder the terms:
18((-4 + 3x)(-4 + 3x)) = 108

Multiply (-4 + 3x) * (-4 + 3x)
18((-4(-4 + 3x) + 3x * (-4 + 3x))) = 108
18(((-4 * -4 + 3x * -4) + 3x * (-4 + 3x))) = 108
18(((16 + -12x) + 3x * (-4 + 3x))) = 108
18((16 + -12x + (-4 * 3x + 3x * 3x))) = 108
18((16 + -12x + (-12x + 9x2))) = 108

Combine like terms: -12x + -12x = -24x
18((16 + -24x + 9x2)) = 108
(16 * 18 + -24x * 18 + 9x2 * 18) = 108
(288 + -432x + 162x2) = 108

Solving
288 + -432x + 162x2 = 108

Solving for variable 'x'.

Reorder the terms:
288 + -108 + -432x + 162x2 = 108 + -108

Combine like terms: 288 + -108 = 180
180 + -432x + 162x2 = 108 + -108

Combine like terms: 108 + -108 = 0
180 + -432x + 162x2 = 0

Factor out the Greatest Common Factor (GCF), '18'.
18(10 + -24x + 9x2) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(10 + -24x + 9x2)' equal to zero and attempt to solve:

Simplifying
10 + -24x + 9x2 = 0

Solving
10 + -24x + 9x2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
1.111111111 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.111111111' to each side of the equation.
1.111111111 + -2.666666667x + -1.111111111 + x2 = 0 + -1.111111111

Reorder the terms:
1.111111111 + -1.111111111 + -2.666666667x + x2 = 0 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + -1.111111111
-2.666666667x + x2 = 0 + -1.111111111

Combine like terms: 0 + -1.111111111 = -1.111111111
-2.666666667x + x2 = -1.111111111

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -1.111111111 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -1.111111111 + 1.777777780

Combine like terms: -1.111111111 + 1.777777780 = 0.666666669
1.777777780 + -2.666666667x + x2 = 0.666666669

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 0.666666669

Calculate the square root of the right side: 0.816496582

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 0.816496582 and -0.816496582.

Subproblem 1
x + -1.333333334 = 0.816496582

Simplifying
x + -1.333333334 = 0.816496582

Reorder the terms:
-1.333333334 + x = 0.816496582

Solving
-1.333333334 + x = 0.816496582

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 0.816496582 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 0.816496582 + 1.333333334
x = 0.816496582 + 1.333333334

Combine like terms: 0.816496582 + 1.333333334 = 2.149829916
x = 2.149829916

Simplifying
x = 2.149829916

Subproblem 2
x + -1.333333334 = -0.816496582

Simplifying
x + -1.333333334 = -0.816496582

Reorder the terms:
-1.333333334 + x = -0.816496582

Solving
-1.333333334 + x = -0.816496582

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -0.816496582 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -0.816496582 + 1.333333334
x = -0.816496582 + 1.333333334

Combine like terms: -0.816496582 + 1.333333334 = 0.516836752
x = 0.516836752

Simplifying
x = 0.516836752

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.149829916, 0.516836752}
Solution
x = {2.149829916, 0.516836752}